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Forex traders said the upward trend in crude prices and outflow of foreign funds from equities market restricted the gain in the local unit.
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At the interbank foreign exchange, the domestic unit opened weak at 81.95 against the dollar, registering a decline of 5 paise over its last close. In initial trade, the local unit also saw a high of 81.88 against the greenback.
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At the interbank foreign exchange market, the rupee opened higher at 82.08 against the US dollar and moved in a narrow range of 82.04 to 82.10 later in early deals.
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The rupee had closed lower by 18 paise at 82.34 to a dollar on Wednesday. The forex market was closed on Thursday for Ram Navami.
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BSE Sensex rose by 123.64 points or 0.21 per cent to 57,737.36 while NSE Nifty gained 53.70 points or 0.32 per cent to 17,005.40 in early trade.
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The Indian currency traded between 82.46 and 82.55.
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The 30-share BSE Sensex was trading 403.21 points or 0.70 per cent higher at 58,303.40 points while the broader NSE Nifty was up 130.40 points or 0.77 per cent to 17,173.70 points.
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The dollar index, which gauges the greenback's strength against a basket of six currencies fell 0.77 per cent to 103.78.
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In initial trade, the rupee also touched a low of 82.61 against the American currency
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At the interbank foreign exchange, the domestic unit opened on a strong note at 80.53 against the dollar, then pared the gains to quote at 80.93, registering a loss of 15 paise over its previous close.
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At the interbank foreign exchange, the domestic unit opened at 80.76 against the dollar, then gained further ground to touch 80.69, registering a rise of 71 paise over its previous close.
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Forex traders said the focus will be on the US October CPI print scheduled to be released later on Thursday.
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At the interbank foreign exchange, the domestic unit opened at 82.85 against the dollar, then gained ground to touch 82.63, registering a rise of 25 paise over its previous close.
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At the interbank foreign exchange, the domestic unit opened at 82.15 against the dollar, then gained ground to quote at 82.14, registering a rise of 67 paise over its previous close.
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At the interbank foreign exchange, the domestic unit opened at 82.89 against the dollar, then lost further ground to 82.91, registering a loss of 12 paise over its previous close.
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Various factors such as inflation, interest rates, quantum of public debt and current account deficit influence the dollar-rupee exchange rate to a great extent.
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However, persistent foreign capital outflows capped the gains of the local unit, forex traders said.
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At the interbank foreign exchange, the domestic unit opened lower at 82.33 against the dollar, then lost further ground to quote at 82.38, registering a fall of 19 paise over its previous close.
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Moreover, risk aversion sentiment among investors and weak Asian and emerging market currencies weighed on the local unit.
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Moreover, a negative trend in domestic equities and firm American currency sapped investor appetite, forex traders said.